Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Fractional differentiation and Lipschitz spaces on local fields
HTML articles powered by AMS MathViewer

by C. W. Onneweer PDF
Trans. Amer. Math. Soc. 258 (1980), 155-165 Request permission

Abstract:

In this paper we continue our study of differentiation on a local field K. We define strong derivatives of fractional order $\alpha > 0$ for functions in ${L_r}(\textbf {K})$, $1 \leqslant r < \infty$. After establishing a number of basic properties for such derivatives we prove that the spaces of Bessel potentials on K are equal to the spaces of strongly ${L_r}(\textbf {K})$-differentiable functions of order $\alpha > 0$ when $1 \leqslant r \leqslant 2$. We then focus our attention on the relationship between these spaces and the generalized Lipschitz spaces over K. Among others, we prove an inclusion theorem similar to a wellknown result of Taibleson for such spaces over ${\textbf {R}^n}$.
References
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 43A70, 26A33
  • Retrieve articles in all journals with MSC: 43A70, 26A33
Additional Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 258 (1980), 155-165
  • MSC: Primary 43A70; Secondary 26A33
  • DOI: https://doi.org/10.1090/S0002-9947-1980-0554325-1
  • MathSciNet review: 554325